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Convergence of Singular Integral Operators in Weighted Lebesgue Spaces

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2017

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Abstract (2. Language): 
In this paper, the pointwise approximation to functions f G L1w (a, b) by the convolution type singular integral operators given in the following form: where (a, b) stands for arbitrary closed, semi closed or open bounded interval in R or R itself, L1w (a, b) denotes the space of all measurable but non-integrable functions f for which f is integrable on (a, b) and w : R — R+ is a corresponding weight function, at a ^-generalized Lebesgue point and the rate of convergence at this point are studied.
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REFERENCES

References: 

[1] S E Almali. Convergence and the Order of Convergence of Family of Nonconvolution Type Integral Operators at Characteristic points. Ph. D. Thesis, Ankara University, Graduate School of Applied Science, Ankara, 2002.
[2] C Bardaro and C G Cocchieri. On the Degree of Approximation for a Class of Singular Integrals. Rend. Mat., 7(4):481-490, 1984.
[3] C Bardaro. On Approximation Properties for Some Classes of Linear Operators of Convolution Type. Atti Sem. Mat. Fis. Univ. Modena, 33(2):329-356, 1984.
[4] C Bardaro and I Mantellini. Pointwise Convergence Theorems for Nonlinear Mellin Convolution Operators. Int. J. Pure Appl. Math., 27(4):431-447, 2006.
[5] C Bardaro, H Karsli and G Vinti. On Pointwise Convergence of Linear Integral Operators with Homogeneous Kernel. Integral Transforms and Special Functions, 19(6):429-439, 2008.
[6] C Bardaro, G Vinti and H Karsli. Nonlinear Integral Operators with Homogeneous Kernels: Pointwise Approximation Theorems. Appl. Anal., 90(3-4):463-474, 2011.
[7] C. Bardaro, H. Karsli and G. Vinti, On pointwise convergence of Mellin type nonlinear m-singular integral operators, Comm. Appl. Nonlinear Anal. 20, 2(2013), 25-39.
[8] P L Butzer and R J Nessel. Fourier Analysis and Approximation: Vol. I. Academic Press, New York, London, 1971.
[9] A D Gadjiev. The Order of Convergence of Singular Integrals which Depend on Two Param¬eters. In Special Problems of Functional Analysis and their Appl. to the Theory of Diff. Eq. and the Theory of Func., Izdat. Akad. Nauk Azerbaıdazan. SSR., pages 40-44, 1968.
[10] H Karsli and E Ibikli. Approximation Properties of Convolution Type Singular Integral Op¬erators Depending on Two Parameters and of Their Derivatives in L1(a,b). In Proc. 16 th Int. Conf. Jangjeon Math. Soc., 16:66-76, 2005.
[11] H Karsli. Convergence and Rate of Convergence by Nonlinear Singular Integral Operators Depending on Two Parameters. Appl. Anal., 85(6-7):781-791, 2006.
[12] H Karsli and E Ibikli. On Convergence of Convolution Type Singular Integral Operators Depending on Two Parameters. Fasc. Math., 38:25-39, 2007.
[13] H Karsli. On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators. Georgian Math. J., 15:77-86, 2008.
[14] R G Mamedov. On the Order of Convergence of m-Singular Integrals at Generalized Lebesgue Points and in the Space Lp(-oo, oo). Izv. Akad. Nauk SSSR Ser. Mat., 27(2):287-304, 1963.
[15] B Rydzewska. Approximation des Fonctions par des Integrales Singulieres Ordinaires. Fasc.
Math., 7:71-81, 1973.
REFERENCES 347
[16] R Taberski. Singular Integrals Depending on Two Parameters. Prace Mat., 7:173-179, 1962

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